$0.86. You either divide by 10 manually, or use the powers of 10.
Answer:
x = -4/5 and -1/2
Step-by-step explanation:
"Finding zeroes" means find the x-values that make f(x) = 0, so we have...
0 = 10x² + 9x + 2
Use quadratic equation to solve...
x = [-9 ± √(9² - 4(10)(2))]/[2(10)]
x = [-9 ± √(81 - 80)]/20
x = [-9 ± √1]/20
x = [-9 ± 1]/20
x = (-9 + 1)/20 and (-9 - 1)/20
x = -8/20 and -10/20
x = -4/5 and -1/2
The answer is 10 2/3, 5
Proof:
Solve the following system:
{x/2 + y/3 = 7 | (equation 1)
{x/4 + (2 y)/3 = 6 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{x/2 + y/3 = 7 | (equation 1)
{0 x+y/2 = 5/2 | (equation 2)
Multiply equation 1 by 6:
{3 x + 2 y = 42 | (equation 1)
{0 x+y/2 = 5/2 | (equation 2)
Multiply equation 2 by 2:
{3 x + 2 y = 42 | (equation 1)
{0 x+y = 5 | (equation 2)
Subtract 2 × (equation 2) from equation 1:
{3 x+0 y = 32 | (equation 1)
{0 x+y = 5 | (equation 2)
Divide equation 1 by 3:
{x+0 y = 32/3 | (equation 1)
{0 x+y = 5 | (equation 2)
Collect results:
Answer: {x = 10 2/3, y = 5
Answer:
40
Step-by-step explanation:
Use Pythagorean Theorem to find the 3rd side, which will be 17. Then add all of the sides and you'll get the answer.
Answer:
the probability is 0.311 (31.1%)
Step-by-step explanation:
defining the event L= being late to work :Then knowing that each mode of transportation is equally likely (since we do not know its travel habits) :
P(L)= probability of taking the bicycle * probability of being late if he takes the bicycle + probability of taking the car* probability of being late if he takes the car + probability of taking the bus* probability of being late if he takes the bus +probability of taking the train* probability of being late if he takes the train = 1/4 * 0.75 + 1/4 * 0.43 + 1/4 * 0.15 + 1/4 * 0.05 = 0.345
then we can use the theorem of Bayes for conditional probability. Thus defining the event C= Bob takes the car , we have
P(C/L)= P(C∩L)/P(L) = 1/4 * 0.43 /0.345 = 0.311 (31.1%)
where
P(C∩L)= probability of taking the car and being late
P(C/L)= probability that Bob had taken the car given that he is late
